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					The Economics of Moral Hazard: Comment

         Mark V. Pauly

         The American Economic Review, Vol. 58, No. 3, Part 1. (Jun., 1968), pp. 531-537.

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                               COMMUNICATIONS                                       53 1

   Second, hiishan's use of taxes and subsidies as i~zccfztiveso internalize ex-
                                                               t
ternality is not clear. I n section 11, he employs variable taxes or subsidies to
transform the opportunity locus of X and k' onto the appropriate marginal
evaluation curve. However, this will not, contrary to hlishan's expectation, in-
duce either to select the intersection of the curves over other (equally desir-
able) points along the appropriate marginal evaluatioil curve. Since neither is
being made better off, neither has an incentive to maximize. The intersection
could be induced through lump sum transfers combined with a per-unit tax (or
subsidy) on X.
   Finally, Mishan considers whether it will be simple to regulate externality
with a tax system. I agree that it is a practical matter. He suggests the prob-
lem is likely to be small because the welfare effects of the internalizing tech-
nique will be small. However, in some real world cnses that come to mind
(e.g., Pauly's example of water pollution), compensation a t marginal damage
rates leads to considerable deviation from exact compensation.
                                                   F. TRENERY   DOLBEAR,  JR.*

  * T h e author is a Brookings Economic Policy Fellow at the C.S. Bureau of the Budget.



              The Economics of Moral Hazard: Comment
   When uncertainty is present in economic activity, insurance is commonly
found. Indeed, Kenneth .Arrow [ l ] has identified a kind of market failure
with the absence of markets to provide insurance against some uncertain
events. Arrow stated that "the welfare case for insurance of all sorts is over-
whelming. I t follows that the government should undertake insurance where
the market, for whatever reason, has failed to emerge" [ I , pp. 935, 9611.
This paper will show, however, that even if all individuals are risk-averters,
insurance against some types of uncertain events may be nonoptimal. Hence,
the fact that certain kinds of insurance have failed to emerge in the private
market may be no indication of nonoptimality, and compulsory government
insurance against some uncertain events may lead to inefficie:lcy. I t will also
be shown that the problem of "moral hazard" in insurance has, in fact, little
to do with morality, but can be analyzed with orthodox economic tools.
   The particular type of insurance for which the argument will be presented
is that of insurance against medical care expenses, for it was in a discussion of
medical expense insurance that Arrow framed the propositions cited above.
However, the analysis is applicable as well to other types of insurance, such as
automobile collision insurance.
                   I. The Welfare Implications o Insz~rarzce
                                                   f
   I t is assumed that all individuals are expected utility maximizers and are
risk-averters, and that the incidence of illness is a random event. This ex-
cludes preventive medicine from consideration, and it also ignores the effect
that medical insurance might have on the purchase of preventive care. Ber-
noulli's theorem, as cited b17 Arrov [ I , pp. 959-611, states that such individ-
532                THE AMERICAN ECONOMIC REVIEW
uals will prefer insurance with a premium m which indemnifies against all
costs of medical care to facing without insurance a probability distribution of
such expenditures with mean m.
   There is a social gain obtained by purchase of this insurance (as long as
the insurer suffers no social loss) since pooling of risks reduces the total risk,
and therefore the risk per insured, because of the Law of Large Numbers. Of
course, the existence of transactions costs means that the policy is not really
offered at the actuarially fair premium m. However, since the individual pre-
ferred actuarially fair insurance to self-insurance, he will prefer some insur-
ance with an actuarially unfair premium to self-insurance, so long as the pre-
mium is not too "unfair." His preference in this regard will depend on the
intensity of his risk aversion and the strength of the Law of Large Numbers
in reducing risk.
   As indicated above, Arrow concluded from this analysis that the absence of
commercial insurance against some uncertain medical-care expenses provides a
case for government intervention to provide such insurance. Dennis Lees and
R. D. Rice [ 6 ] answered that this insurance was not offered because of sell-
ing and transactions costs. Arrow [ 2 1 replied, in effect, that such costs were
dead-weight losses anyway, and indeed would be eliminated by compulsory so-
cial insurance. I t seems clear, however, that there is another and better way to
explain why some insurances are not offered commercially. I t is to show that
some, perhaps many, medical care expenses are not "insurable" in the stan-
dard sense.
   In order for the welfare proposition given above to be valid, the costs of
medical care must be random variables. But if such expenses are not com-
pletely random, the proposition no longer holds. The quantity of medical care
an individual will demand depends on his income and tastes, how ill he is, and
the price charged for it. The effect of an insurance which indemnifies against
all medical care expenses is to reduce the price charged to the individual at
the point of service from the market price to zero. Even if the incidence of
illness is a random event, whether the presence of insurance will alter the ran-
domness of medical expenses depends on the elasticity of demand for medical
care. Only if this demand is perfectly inelastic with respect to price in the
 range from the market price to zero is an expense "insurable" in the strict
sense envisioned by Arrow's welfare proposition.
   Suppose, for example, that an individual faces the probability p, = f/2 that
 he will not be sick at all during a given time period (event I,) and so will
 demand no medical care, probability p, =        that he will contract sickness I,,
 and probability p3 =       that he will contract "more serious" sickness I,. The
 position of his demand curve for medical care depends on which illness, if any,
 he contracts. In Figure 1, it is assumed that his demand curves D2 and D,
 are perfectly inelastic, and that his demand curve for the "no illness" case is
 identical with the y-axis. Without insurance, the individual faces the probability
 p, that he will incur no medical expenses, the probability pz that he will need
 50 units of medical care (which is assumed to be priced at marginal cost), and
 the probability p, that he will need 200 units of medical care at a cost of 200
MC. The mean of this probability distribution (or the expected values of the
                                 COMMUNICATIONS 

          Price or Cost




individual's medical care expenses) equals         (s
                                                   /2 0        ++X 50 M C        %    +
X 200 M C ) or 62.5 MC. Hence, an actuarially fair insurance which in-
demnifies the individual against all costs of medical care could be offered at a
premium P of 62.5 MC. Arrow's welfare proposition indicates that the indi-
vidual would prefer paying a premium of 62.5 M C to risking the probability
distribution with the mean m = 62.5 MC.
   Suppose, however, that the individual's demand curves are not all perfectly
                        ,
inelastic, but are as D ' and D,'. Then the individual has to choose between
facing, without insurance, the probability distribution ( % X 0               +
                                                                          T/ii X 50
MC   +    f X 200 M C ) with a mean m of 62.5 MC, and paying a premium
of P =   (s + /2 0     f X 150 M C         +
                                          % /4 300 M C ) = 112.5 M C in order
to obtain insurance. I n such a case, he may well prefer the risk to the insurance.
   The presence of elasticity in the demand curves implies therefore that the
individual will alter his desired expenditures for medical care because of the
fact of insurance. The individual who has insurance which covers all costs de-
mands medical care as though it had a zero price, but when he purchases in-
surance, he must take account of the positive cost of that care, as "translated"
to him through the actuarially necessary premium. Hence, he may well not
wish to purchase such insurance at the premium his behavior as a purchaser
of insurance and as a demander of medical care under insurance makes
neces~ary.~
  'This is exactly the same sort of "inconsistency" that Buchanan has ncted in connect~on
with the British National Health Service. Individuals demand medical care as though it
were free but in voting decisions consider the positive cost of such care. Hence, they vote,
through their representatives in the political process, to provide facilities for less medical
care than they demand in the market. See [41.
534                    TI-IE AMERICAN ECONOMIC REVIEW

   The presence of a "prisoners' dilemma" motivation makes this inconsis-
tency inevitable."ach      individual may well recognize that "excess" use of
medical care makes the premium he must pay rise. No individual will be moti-
vated to restrain his own use, however, since the incremental benefit to him
for excess use is great, while the additional cost of his use is largely spread
over other insurance holders, and so he bears only a tiny fraction of the cost
of his use. I t would be better for all insurance beneficiaries to restrain their
use, but such a result is not forthcoming because the strategy of "restrain use"
is dominated by that of "use excess care."
    If the demand for medical care is of greater than zero elasticity, the exis-
tence of this "inconsistency" implies that inefficiency may well be created if
individuals are forced, by taxation, to "purchase" insurance which indemnifies
against some kinds of medical care expense. For an efficient solution, at least
some price-rationing at the point of service may be necessary.
   Suppose there are no significant income effects on the individual's demand
for medical care resulting from his payment of a lump-sum premium for insur-
ance. In Figure 1, the ineEciency loss due to behavior under insurance, if that
insurance were compulsory, would then be roughly measured by triangles
ABC and DEF. These areas represent the excess that individuals do pay over
                   be
what they ~ o u l d willing to pay for the quantity of medical care demanded
under insurance. Against this loss must be offset the utility gain from having
these uncertain expenses insured, but the net change in utility from a compul-
sory purchase of this "insurance" could well be negative.
   Moreover, if individual demands for medical care differ, it is possible that
the loss due to "excess7' use under insurance may exceed the welfare gain from
insurance for one individual but fall short of it for another individual. I t fol-
lows that it may not be optimal policy to provide compulsory insurance
against particular events for all individuals. Some events may be "insurable"
for some persons but not for others. I t also follows that some events, though
uncertain, may not be insurable for anyone. If persons differ (a) in the
strength of their risk aversion or (b) in the extent to which insurances of var-
ious types alter the quantity of medical care they demand, an optimal state
will be one in which various types of policies are purchased by various groups
of people. There may be some persons who will purchase no insurance against
some uncertain events.
   Insurance is more lil~elyto be provided against those events (a) for which
the quantity demanded at a zero price does not greatly exceed that demanded
a t a positive price, (b) for which the extent of randomness is greater, so that
risk-spreading reduces the risk significantly, and (c) against which individuals
have a greater risk-aversion. There is uncertainty attached to "catastrophic7'
illness, but it appears that the elasticity of demand for treatment against such
illness is not very great (in the sense that there is one and only one appropriate
tre?.tment). Furthermore, the "randonlness" attached to such illnesses is rela-
tively great, in the sense that they are unpredictable for any individual, and
people's aversion to such risk is relatively great. Hence, one would expect to
  ' For a discussion   of the prisoners' dilemma problem, see [ i l .
                                 COMMUNICATIONS                                         535

find, and does find, insurance orlered against such e\lents. Similar statement
might be made with respect to ordinary hospitalization insurance.
   There is also some uncertainty attached to visits to a physician's office, but
the extent of randomness and risk-aversion is probably relatively low for most
persons. The increase in use in response to a zero price would be relatively
great. One would not expect to find, and does not in general find, "insurance"
against such events. Similar analysis applies to insurance against the cost of
dental care, eyeglasses, or drugs.

                                 1 . Moral Hazard
                                  1
   I t has been recognized in the insurance literature that medical insurance,
by lowering the marginal cost of care to the individual, may increase usage;
this characteristic has been termed "moral hazard." Moral hazard is defined
as "the intangible loss-producing propensities of the individual assured" [4,
p. 4631 or as that which "comprehends all of the nonphysical hazards of risk"
[S, p. 421. Insurance writers have tended very strongly to look upon this
phenomenon (of demanding more at a zero price than at a positive one) as a
moral or ethical problem, using emotive words such as "malingering" and "hy-
pochondria," lumping it together with outright fraud in the collection of bene-
fits, and providing value-tinged definitions as "moral hazard reflects the haz-
ard that arises from the failure of individuals who are or have been affected by
insurance to uphold the accepted moral qualities" [ 5 , p. 3271, or "moral haz-
ard is every deviation from correct human behavior that may pose a problem
for an insurer" [3, p. 2 2 1 . It is surprising that very little economic analysis
seems to have been applied here.3
   The above analysis shows, however, that the response of seeking more med-
ical care with insurance than in its absence is a result not of moral perfidy,
but of rational economic behavior. Since the cost of the individual's excess
usage is spread over all other purchasers of that insurance, the individual is
not prompted to restrain his usage of care.

                      1 1 Deductibles and Coi?zsurance
                       1.
  The only type of insurance so far considered has been an insurance which
provides full coverage of the cost of medical care. However, various devices
are written into insurance, in part to reduce the moral hazard, of which the
most important are deductibles and coin~urance.~ individual may well
                                                    The

  "n his original article, Arrow mentions moral hazard as a "practical limitation" on the
use of insurance which does not "alter the case for creation of a much wider class of insur-
ance policies than now exist" [ I , p. 9611. However, Arrow appears to consider moral
hazard as an imperfection, a defect in physician control, rather than as a simple response
to price reduction. I-Ie does not consider the direct relationship u hich exists between the
existence of moral hazard and the vaiidity of the welfare proposition. More importantly, in
the controversy that folloned [21 [61, moral hazard seems to have been completely over-
looked as an explanation oi why certain types of expenses are not insured commercially.
  ' A deductible is the exclusion of a certain amount of expense from coverage; coinsurance
requires the individual to pnv some fraction of each dollar of cost
536                THE AMERICAN ECONOMIC REVIEW
prefer no insurance to full coverage of all expenses, but may at the same time
prefer an insurance with these devices to no i n ~ u r a n c e . ~
A. 	Deductibles
   Suppose the insurance contains a deductible. The individual will compare
the position he would attain if he covered the deductible and received addi-
tional care free with the position he would attain if he paid the market price
for all the medical care he consumed but did not cover the deductible. If in-
come effects are absent in Figure 1, the individual will cover a deductible and
consume 150 units of medical care when event I z occurs as long as the "ex-
cess" amount he pays as a deductible (e.g., area AGH for a deductible of 75
MC) is less than the consumer's surplus he gets from the "free" units of care
                                                           f
this coverage allows him to consume (e.g., area HJB). I the deductible ex-
ceeds 100 M C (at which point area AG'H' equals area H'J'B), the individual
will not cover the deductible and will purchase 50 units. Hence, the deducti-
ble either ( a ) has no effect on an individual's usage or (b) induces him to
consume that amount of care he would have purchased if he had no insurance.
 f
I there are income effects on individual demands, because the deductible
malres the individual poorer his usage will be restrained somewhat even if he
covers the deductible.
B. 	Coinsurance
   Coinsurance is a scheme in which the individual is, in effect, charged a posi-
tive price for medical care, but a price less than the market price. The higher
the fraction paid by the individual, the more his usage will be curtailed. I n
Figure 1, if he had to pay OL of each unit's cost, he would reduce his usage if
event I, occurred from 150 units to 75 units. The smaller the price elasticity
of demand for medical care, the less will be the effect of coinsurance on
usage.
   I t is possible for the restraining effect of coinsurance to reduce moral haz-
ard enough to make insurance attractive to an individual who would have pre-
ferred no insurance to full-coverage insurance. Indeed, there is an optimal ex-
tent of coinsurance for each individual. The optimal extent of coinsurance is
the coverage of that percentage of the cost of each unit of medical care at
which the utility gain to the individual from having an additional small frac-
tion of the cost of each unit of care covered by insurance equals the utility
loss to him upon having to pay for the "excess" units of care whose consump-
                                              f
tion the additional coverage encourages. I the marginal gain from the cover-
age of additional fractions of cost always exceeds the marginal inefficiency
loss, he will purchase full coverage insurance; if the marginal loss exceeds the
marginal gain for all extents of coinsurance, the individual will purchase no
insurance. I individual demands differ, the optimal extent of coinsurance will
             f
differ for different individuals.
  'Arrow [I, pp. 969-731 gives some other arguments to explain why the individual will
prefer insurance with deductibles or coinsurance t o insurance without such devices.
                                COMMUNICATIONS 	                                     537

                                  IV. Conclusion
   I t is possible to conclude that even if all individuals are risk-averters, some
uncertain medical care expenses will not and should not be insured in an opti-
mal situation. No single insurance policy is "best" or "most efficient" for a
whole population of diverse tastes. Wlich expenses are insurable is not an ob-
jective fact, but depends on the tastes and behavior of the persons involved.
                                                                      V.
                                                               MARK PAULY*
  * T h e author is assistant professor of economics at Northwestern University. Research
for this paper was supported in part by a grant from the United States Public Health
Service under the general supervision of Professor James Buchanan.

                                    REFERENCES
1. 	K. J. ARROW,     "Uncertainty and the Welfare Economics of Medical Care,"
     Am. Econ. Rev., Dec. 1963, 53, 941-73.
2.             , "Reply," Am. Econ. REV.,March 1965, 55, 154-58.
3. 	J. M. BUCHANAN,        The Inconsistencies of the National Health Service,
     Inst. of Econ. Affairs Occas. Paper 7. London 1964.
4. 	 0. D. DICKERSON,     Health Insurance, rev. ed. Homewood, Ill. 1963.
5. 	E. J. FAULKNER,     Health Insurance. New York 1960.
6. D. 	S. LEES AND R. G. RICE, "Uncertainty and the Welfare Economics of
     Medical Care: Comment," Am. Econ. Rev., March 1965, 55, 140-54.
7. 	 R. D. LUCEAND H. RAIFFA,Games and Decisions. New York 1957.
8. 	 G. F. MICHELBACHER,      Multiple-line Insurance. New York 1957.



         The Economics of Moral Hazard: Further Comment
   Mr. Pauly's paper [3] has enriched our understanding of the phenomenon
of so called "moral hazard" and has convincingly shown that the optimality of
complete insurance is no longer valid when the method of insurance influences
the demand for the services provided by the insurance policy. This point is
worth making strongly. In the theory of optimal allocation of resources under
risk bearing it can be shown that competitive insurance markets will yield op-
timal allocation when the events insured are not controllable by individual be-
havior. I the amount of insurance payment is in any way dependent on a
          f
decision of the insured as well as on a state of nature, then the effect is very
much the same as that of any excise tax and optimality will not be achieved
either by the competitive system or by an attempt by the government to sim-
ulate a perfectly competitive system. For some earlier, less detailed, discus-
sions of this point see [I,pp. 55-56], [ Z , pp. 961-621.
   In this note, I would like to stress a point which Mr. Pauly overlooks in his
exclusive emphasis on market incentives. Mr. Pauly has a very interesting sen-
tence: "The above analysis shows, however, that the response of seeking more
medical care with insurance than in its absence is a result not of moral per-
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You have printed the following article:
        The Economics of Moral Hazard: Comment
        Mark V. Pauly
        The American Economic Review, Vol. 58, No. 3, Part 1. (Jun., 1968), pp. 531-537.
        Stable URL:
        http://links.jstor.org/sici?sici=0002-8282%28196806%2958%3A3%3C531%3ATEOMHC%3E2.0.CO%3B2-A



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[Footnotes]

    3
     Uncertainty and the Welfare Economics of Medical Care
    Kenneth J. Arrow
    The American Economic Review, Vol. 53, No. 5. (Dec., 1963), pp. 941-973.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196312%2953%3A5%3C941%3AUATWEO%3E2.0.CO%3B2-C

    3
     Uncertainty and the Welfare Economics of Medical Care: Reply (The Implications of
    Transaction Costs and Adjustment Lags)
    Kenneth J. Arrow
    The American Economic Review, Vol. 55, No. 1/2. (Mar. - May, 1965), pp. 154-158.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196503%2F05%2955%3A1%2F2%3C154%3AUATWEO%3E2.0.CO%3B2-8

    3
     Uncertainty and the Welfare Economics of Medical Care: Comment
    Dennis S. Lees; Robert G. Rice
    The American Economic Review, Vol. 55, No. 1/2. (Mar. - May, 1965), pp. 140-154.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196503%2F05%2955%3A1%2F2%3C140%3AUATWEO%3E2.0.CO%3B2-F

    5
     Uncertainty and the Welfare Economics of Medical Care
    Kenneth J. Arrow
    The American Economic Review, Vol. 53, No. 5. (Dec., 1963), pp. 941-973.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196312%2953%3A5%3C941%3AUATWEO%3E2.0.CO%3B2-C
NOTE: The reference numbering from the original has been maintained in this citation list.
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                        LINKED CITATIONS
                                 - Page 2 of 2 -




References

    1
     Uncertainty and the Welfare Economics of Medical Care
    Kenneth J. Arrow
    The American Economic Review, Vol. 53, No. 5. (Dec., 1963), pp. 941-973.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196312%2953%3A5%3C941%3AUATWEO%3E2.0.CO%3B2-C

    2
     Uncertainty and the Welfare Economics of Medical Care: Reply (The Implications of
    Transaction Costs and Adjustment Lags)
    Kenneth J. Arrow
    The American Economic Review, Vol. 55, No. 1/2. (Mar. - May, 1965), pp. 154-158.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196503%2F05%2955%3A1%2F2%3C154%3AUATWEO%3E2.0.CO%3B2-8

    6
     Uncertainty and the Welfare Economics of Medical Care: Comment
    Dennis S. Lees; Robert G. Rice
    The American Economic Review, Vol. 55, No. 1/2. (Mar. - May, 1965), pp. 140-154.
    Stable URL:
    http://links.jstor.org/sici?sici=0002-8282%28196503%2F05%2955%3A1%2F2%3C140%3AUATWEO%3E2.0.CO%3B2-F




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